Transcribed Image Text:List the eigenvalues of \( A \). The transformation \( x \to Ax \) is the composition of a rotation and a scaling. Give the angle \( \phi \) of the rotation, where \( -\pi < \phi \leq \pi \), and give the scale factor \( r \).
\[
A = \begin{bmatrix}
3\sqrt{3} & -3 \\
3 & 3\sqrt{3}
\end{bmatrix}
\]
---
The eigenvalues of \( A \) are \( \lambda = \, \Box \).
(Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals and \( i \) as needed.)
\( \phi = \, \Box \)
(Simplify your answer. Type an exact answer, using \( \pi \) as needed.)
\( r = \, \Box \)
(Simplify your answer.)
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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![List the eigenvalues of \( A \). The transformation \( x \to Ax \) is the composition of a rotation and a scaling. Give the angle \( \phi \) of the rotation, where \( -\pi < \phi \leq \pi \), and give the scale factor \( r \).
\[
A = \begin{bmatrix}
3\sqrt{3} & -3 \\
3 & 3\sqrt{3}
\end{bmatrix}
\]
---
The eigenvalues of \( A \) are \( \lambda = \, \Box \).
(Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals and \( i \) as needed.)
\( \phi = \, \Box \)
(Simplify your answer. Type an exact answer, using \( \pi \) as needed.)
\( r = \, \Box \)
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe763e4e-f795-40b2-8fd9-57a3e5a9095e%2Fd6187730-0c50-49bc-befa-24aa05c59026%2Fpliltoj_processed.png&w=3840&q=75)
